Determining electrical characteristics of an electrical cable

• US 7,586,313 B2
• Filed: 04/26/2007
• Issued: 09/08/2009
• Est. Priority Date: 04/26/2007
• Status: Active Grant

• Current Assignee: Schlumberger Technology Corporation (Schlumberger NV)
• Original Assignee: Schlumberger Technology Corporation (Schlumberger NV)
• Inventors: Rajasekaran, Vinod, Hernandez-Marti, Ramon
• Primary Examiner(s): Dole; Timothy J
• Assistant Examiner(s): Baldridge; Benjamin M
• Application Number:
  US11/740,739
• Publication Number:
  US 20080265898A1
• Time in Patent Office: 866 Days
• Field of Search: 324/538, 324/323
• US Class Current: 324/538
• CPC Class Codes: G01R 31/58 Testing of lines, cables or conductors testing of electric windings G01R31/72
• CPC Class Codes: G01V 11/002 Details, e.g. power supply systems for logging instruments, transmitting or recording data, specially adapted for well logging, also if the prospecting method is irrelevant means for transmitting well survey signals E21B47/12; signal transmission systems in general G08C; transmission in general H04B
• CPC Class Codes: G10K 11/002 Devices for damping, suppressing, obstructing or conducting sound in acoustic devices G10K1/06 - G10K1/10 take precedence; for electro-mechanical transducers for communication H04R3/002

Abstract

To characterize an electrical cable that is deployed in a well, a voltage input is applied to the electrical cable at an earth surface location, where the well extends from the earth surface location. A current response resulting from the voltage input is measured at the earth surface location. At least one parameter of the electrical cable is computed according to the measured current response.

Claims

1. A method of characterizing an electrical cable that is deployed in a well, comprising:

applying a voltage input to the electrical cable at an earth surface location, wherein the well extends from the earth surface location;

measuring a current response in the electrical cable resulting from the voltage input, wherein the current response is measured at the earth surface location; and

computing at least one parameter of the electrical cable according to the measured current response, wherein a load system is connected to a distal end of the electrical cable, and wherein applying the voltage input comprises applying the voltage input that steps from a first voltage level to a second, higher voltage level, wherein the second voltage level is less than an activation voltage for activating the load system.

2. The method of claim 1, wherein the electrical cable is considered open-circuited due to the load system remaining deactivated, wherein applying the voltage input comprises applying the voltage input at an input end of the electrical cable at the earth surface location, and wherein measuring the current resulting from the voltage input is of a current flowing in the electrical cable with a distal end of the cable open-circuited.

3. The method of claim 1, wherein computing the at least one parameter comprises computing a capacitance of the electrical cable by integrating the measured current response over time.

4. The method of claim 3, wherein measuring the current response comprises measuring the current response for the electrical cable having its distal end open-circuited.

5. The method of claim 3, wherein computing the at least one parameter further comprises computing at least one of a resistance and inductance of the electrical cable based on integrating the current response over time.

6. The method of claim 5, wherein computing the resistance, capacitance, and inductance comprises computing resistance R, capacitance C, and inductance L according to:

$\begin{array}{c}\begin{array}{ccc}{A}_0={\int <br><br>}_0^{\mathrm{\infty <br><br>}}<br><br>i<br><br>\left(t\right)<br><br>d<br><br>t;<br><br>& A_1={\int <br><br>}_0^{\mathrm{\infty <br><br>}}<br><br>t<br><br><br><br>i<br><br>\left(t\right)<br><br>d<br><br>t;<br><br>& A_2={\int <br><br>}_0^{\mathrm{\infty <br><br>}}<br><br>t^2<br><br>i<br><br>\left(t\right)<br><br>d<br><br>t\end{array}\\ \begin{array}{ccc}C=\frac{A_0}{V};<br><br>& R=\frac{3<br><br>A_1<br><br>V}{A_0^2};<br><br>& L=\frac{3<br><br>V}{2<br><br>A_0}<br><br>\left(\frac{12}{5}<br><br>\frac{A_1^2}{A_0^2}-\frac{A_2}{A_0}\right),\end{array}\end{array}$

wherein i(t) is the current response, t represents time, and V is a voltage level of the voltage input.

7. The method of claim 6, wherein the input voltage is a step voltage that steps from a first voltage level to a second voltage level, wherein computing the resistance, capacitance, and inductance comprises computing resistance R, capacitance C, and inductance L according to:

$\begin{array}{c}\begin{array}{ccc}{A}_0={\int <br><br>}_0^{\mathrm{\infty <br><br>}}<br><br>i<br><br>\left(t\right)<br><br>d<br><br>t;<br><br>& A_1={\int <br><br>}_0^{\mathrm{\infty <br><br>}}<br><br>t<br><br><br><br>i<br><br>\left(t\right)<br><br>d<br><br>t;<br><br>& A_2={\int <br><br>}_0^{\mathrm{\infty <br><br>}}<br><br>t^2<br><br>i<br><br>\left(t\right)<br><br>d<br><br>t,\end{array}\\ C=\frac{A_0}{V},\\ R=\frac{3<br><br>V}{A_0}<br><br>\left(\frac{A_1}{A_0}-\frac{t_1}{2}\right),\\ L=\frac{3}{2<br><br>C}<br><br>\left(\frac{t_1^2}{3}+\frac{4}{15}<br><br>{\left(\mathrm{RC}\right)}^2-\frac{1}{3}<br><br>\left(\mathrm{RC}\right)<br><br>t_1-\frac{A_2}{A_0}\right),\end{array}$

wherein i(t) is the current response, t represents time, V is the differential voltage between the first and second voltage levels, and t₁ is a rise time of the voltage input from the first voltage level to the second voltage level.

8. The method of claim 1, wherein computing the at least one parameter comprises computing a resistance of the electrical cable by dividing a voltage level of the voltage input by a steady state current flowing in the electrical cable, and wherein measuring the current response comprises measuring the current response for the electrical cable having its distal end short-circuited.

9. The method of claim 8, further comprising:

identifying a first current value of the current response at a first time point;

identifying a second current value of the current response at a second time point;

wherein computing the at least one parameter further comprises computing a capacitance of the electrical cable based on the computed resistance, the first and second current values, the first and second time points, and the steady state current.

10. The method of claim 9, wherein computing the resistance and capacitance comprises computing a resistance R and a capacitance C according to

$R=V/I$

( ∞

) , and $\mathrm{RC}=\frac{6<br><br>\left(t_2-t_1\right)}{\ln <br><br>\left(\frac{I_1-I<br><br>\left(\mathrm{\infty <br><br>}\right)}{I_2-I<br><br>\left(\mathrm{\infty <br><br>}\right)}\right)},$

where V is a voltage level of the voltage input, I(∞

) is the steady state current, I₁ is the first current value, I₂ is the current value, t₁ is the first time point, and t₂ is the second time point.

11. The method of claim 1, further comprising:

deriving a model of the electrical cable using the computed at least one parameter.

12. The method of claim 11, further comprising controlling a voltage applied at a load connected to a distal end of the electrical cable using the derived model.

13. The method of claim 1, further comprising updating the at least one parameter to account for a change in a characteristic of the electrical cable as a result of operation of a load system connected to a distal end of the electrical cable.

14. An apparatus for characterizing an electrical cable that is deployed in a well, comprising:

a voltage input source to apply a step voltage to a first end of an electrical cable wherein a load system is connected to a distal end of the electrical cable, wherein the step voltage comprises a voltage input that steps from a first voltage level to a second, higher voltage level, and wherein the second voltage level is less than an activation

voltage for activating the load system; and

a cable parameter estimator coupled to the voltage input source, the cable parameter estimator to;

measure a current response of the electrical cable resulting from the applied step voltage, wherein the current response is measured at the first end of the electrical cable;

compute at least two parameters of the electrical cable according to the current response.

15. The apparatus of claim 14, wherein the current response is a current response for the electrical cable having an open-circuited distal end.

16. The apparatus of claim 15, wherein the at least two parameters comprises at least two of a resistance, an inductance, and a capacitance, and wherein the resistance, the inductance, and the capacitance are computed based on integrating the current response over time.

17. The apparatus of claim 14, wherein the current response is a current response for the electrical cable having a short-circuited distal end, wherein at least one parameter comprises a resistance computed based on dividing a voltage level of the step voltage by a steady state current and wherein at least one parameter comprises a capacitance computed based on the computed resistance and on a transient portion of the current response.

18. The apparatus of claim 17, wherein the distal end of the cable is short-circuited by connecting windings of a transformer to at least two conductors of the electrical cable.

19. A computer-readable medium containing a set of instructions that when executed cause a computer to:

receive a voltage input applied at a first end of an electrical cable that is deployed in a well;

receive a current response measured at the first end of the electrical cable and that results from the applied voltage input; and

compute at least two parameters of the electrical cable according to the current response, wherein a load system is connected to a distal end of the electrical cable, wherein the voltage input comprises a step voltage that steps from a first voltage level to a second, higher voltage level, and wherein the second voltage level is less than an activation voltage for activating the load system.

20. The article of claim 19, wherein computing the at least one parameter comprises computing a capacitance of the electrical cable and at least one of a resistance and inductance of the electrical cable by integrating the current response over time.

21. The article of claim 20, wherein the current response is the current response for the electrical cable having its distal end open-circuited.

22. The article of claim 19, wherein computing the at least two parameters comprises computing a resistance of the electrical cable by dividing a voltage level of the voltage input by a steady state current flowing in the electrical cable, and wherein the current response is the current response for the electrical cable having its distal end short-circuited.

23. The article of claim 22, wherein the distal end of the cable is short-circuited by connecting windings of a transformer to at least two conductors of the electrical cable.